Question: Solve for $x$ and $y$ using elimination. ${2x+4y = 24}$ ${-3x+5y = -3}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${6x+12y = 72}$ $-6x+10y = -6$ Add the top and bottom equations together. $22y = 66$ $\dfrac{22y}{{22}} = \dfrac{66}{{22}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {2x+4y = 24}\thinspace$ to find $x$ ${2x + 4}{(3)}{= 24}$ $2x+12 = 24$ $2x+12{-12} = 24{-12}$ $2x = 12$ $\dfrac{2x}{{2}} = \dfrac{12}{{2}}$ ${x = 6}$ You can also plug ${y = 3}$ into $\thinspace {-3x+5y = -3}\thinspace$ and get the same answer for $x$ : ${-3x + 5}{(3)}{= -3}$ ${x = 6}$